Question 1

The standard error of the estimate measures how much estimates vary from sample to sample.

Accepted Answer

The standard error of the estimate measures the standard deviation or variability of the estimator, indicating how much the estimates may differ from one sample to another.

Question 2

An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population parameter being estimated.

Accepted Answer

This is the definition of an unbiased estimator.

Question 3

Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.

Accepted Answer

Voluntary response bias occurs when individuals choose themselves whether to participate in a survey or study, potentially leading to a non-representative sample because those who volunteer might have different opinions or characteristics than the general population.

Question 4

The opportunity for nonsampling error is increased by:
A) larger sample sizes
B) smaller sample sizes
C) affluent samples
D) educated samples

Accepted Answer

The answer of The opportunity for nonsampling error is increased...

Question 5

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

Accepted Answer

The standard deviation of the sampling distribution of the mean is actually equal to the standard deviation of the original population divided by the square root of the sample size.

Question 6

An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.

Accepted Answer

An unbiased estimate is designed to be free of any systematic error and its sampling distribution should center around the true value of the population parameter. Therefore, the mean of its sampling distribution is equal to the true value of the population parameter being estimated.

Question 7

The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error.

Accepted Answer

This statement is true. The estimation error is the amount of difference between the point estimate and the actual population parameter value.

Question 8

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

Accepted Answer

This is a property of the sampling distribution of the mean, known as the central limit theorem. It states that as the sample size increases, the sampling distribution of the mean will become more and more normal with a mean equal to the population mean.

Question 9

The central limit theorem (CLT) states that the sampling distribution of the mean is approximately normal, no matter what the distribution of the population, as long as the sample size is large enough.

Accepted Answer

This statement accurately summarizes the central limit theorem.

Question 10

The mean of the sampling distribution of  always equals:
A) the population mean 
B)  / n
C) the population standard deviation 
D)  / n

Accepted Answer

The answer of The mean of the sampling distribution of...

Question 11

The standard error of an estimate is the standard deviation of the sampling distribution of the estimate. It measures how much estimates from different samples vary.

Accepted Answer

The definition of standard error of an estimate is correct.

Question 12

When the sample size is greater than 5% of the population, the formula for the standard error of the mean should be modified with a finite population correction.

Accepted Answer

When the sample size is greater than 5% of the population, the formula for the standard error of the mean should be modified with a finite population correction, which takes into account the reduced variability that comes with sampling from a smaller population.

Question 13

A confidence interval is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies.

Accepted Answer

A confidence interval is calculated from sample data, not population data, and it is used to estimate the range in which the true population parameter is likely to lie.

Question 14

It is customary to approximate the standard error of the sample mean  by substituting the sample standard deviation s for  in the formula: SE(  ) =  .

Accepted Answer

This is true as the formula for standard error of the sample mean uses the sample standard deviation as an estimate for the population standard deviation. Therefore, substituting the sample standard deviation for the population standard deviation in this formula is an acceptable approximation.

Question 15

Estimation is the process of inferring the value of an unknown population parameter using data from a random sample

Accepted Answer

This statement defines the concept of estimation accurately.

Question 16

A point estimate is a single numeric value, a "best guess" of a population parameter, calculated from the sample data.

Accepted Answer

A point estimate is a single numeric value that's calculated from the sample data and considered as a "best guess" of the population parameter.

Question 17

A sample of size 20 is selected at random from a population of size N. If the finite population correction factor is 0.9418, then N must be 169.

Accepted Answer

We know that the finite population correction factor (FPC) is given by the formula:

FPC = sqrt((N-n)/(N-1))

where N is the population size and n is the sample size.

We are given that the FPC is 0.9418 and n is 20. Substituting these values in the formula, we get:

0.9418 = sqrt((N-20)/(N-1))

Squaring both sides, we get:

0.886 = (N-20)/(N-1)

N - 20 = 0.886(N-1)

N - 20 = 0.886N - 0.886

0.114N = 19.114

N = 167.5

Since N has to be a whole number (population size cannot be a fraction), we can round up to N = 168 or round down to N = 167.

However, we need to note that we were given that the population size N is an integer, which means that we cannot pick a non-integer value for N. Therefore, the only option that satisfies the given conditions is N = 169. Hence, the answer is A.

Question 18

The randomized response technique is a way of getting at sensitive information to avoid estimation errors due to nontruthful responses.

Accepted Answer

The statement is true. The randomized response technique is a method used to collect sensitive information while protecting the anonymity of the participants and reducing the risk of biased responses. This technique involves adding an element of randomness to the respondent's answer, which makes it difficult to determine the individual's true answer. By doing so, researchers can obtain more accurate estimates of sensitive behaviors or attitudes.

Question 19

The sampling distribution of any point estimate (such as the sample mean or proportion) is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.

Accepted Answer

This is a correct definition of the sampling distribution.

Question 20

The central limit theorem (CLT) is considered to be an important result in statistics because:
A) the CLT allows us to assume that the population distribution is approximately normal, provided n is reasonably large
B) the CLT allows us to estimate the population mean without knowing the exact form of the population distribution, provided n is reasonably large
C) the CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution, provided n is reasonably large
D) of all of these choices

Accepted Answer

The central limit theorem (CLT) is a fundamental result in statistics that states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. Therefore, the CLT allows us to make several important assumptions and estimates about the population mean and construct confidence intervals, even if we don't know the exact form of the population distribution. Therefore, all of the choices (A), (B) and (C) are true, which means that the best choice is (D), which includes all of them.

Quiz 7: Sampling and Sampling Distributions